Saint Trophime Cathedral door gate, Arles, was build about 1170. In the inner part of the arch we see Jesus and symbols of the four Evangelists. All around them two rows of identical angels with open arms are sculpted, while at the top three different angels play horns or Oliphants. The angels at both sides are ordered in two rows of nine, 18 on the right and 18 on the left. They represent the nine angelic choirs, every choir counting four individuals. The three angels at the top are dancing and blowing into their horns, the outer instruments decorated with seven simple lines, the one in the middle, half broken, without decorations. The two lateral angels are lying backwards in a very uncomfortable position with their legs widely open, while the central one is standing steadily on both feet.

The frame on which all angels lay is made of six ledges. The outer one, thicker than the others, is the extrados of the arch. There are 5 ledges left. The angels of the inner row lay their heads on the second ledge, covering the first and the third with their wings and arms. The angels of the outer row lay their heads in the space between the fourth and the fifth ledge. Musicians feet and wings reach first and fifth ledges.

Since this set of 5 ledges recalls us a pentagram, we are tempted to look for musical notes: angels heads could be considered as such. If we suppose that the first horn on the left is a key of C, the angels in the middle have their heads on G and A and B, all angels on the first or inner row indicate D (except two on E), those of the second row indicate B. So we have the following sequences: D-E, one tone, D-G, a fourth, D-A, a fifth, E-G, minor third and G-B, major third, D-B, the hexachord. The feet of the lateral musicians mark the octave span from C to c.

Then we should observe that angels ordered in rows are all identical but three:

the fourth of the outer row on the right, keeping his right wing considerably bent towards hims

the second angel of the inner row on the right is bending his head to the left side, while all the others keep their head straight in the center;

the first one of inner row on the left bends his head to the right, while all the others keep their head straight in the center.

We can consider these irregularities as a way to show basic musical ratios.

Starting from the right and moving to left on the outer row we count 5 angels, then we meet the angel with a bent wing and we count 4 angels, arriving to the 3 musicians. Thus we have three main ratios: 5/4, 4/3 and 5/3, that are the major third, the fourth, the major sixth or hexachord.

Then starting from the first irregular angel on the left and proceeding to the right on the inner row we count this angel plus the 3 musicians plus 2 angels including the irregular one on the right. Their sum is 6. Thus we have 3/2 and 6/5, the fifth and the minor third.

From the center, left to right again, we find 9 angels versus 8 angels on the inner right row, that gives 9/8, the Tone.

This way we have found the same intervals indicated by the heads of the angels on the pentagram.

Finally, we divide the total of 39 angels into two groups as equal as possible: 20 and 19. 20/19 is one of the ratios used by Boethius to indicate the semitone (De institutione musice, lib.4, XIII).